A190315 Central coefficients of the Riordan matrix ((1-x-x^2)/(1-2x-x^2),(x-x^2-x^3)/(1-2x-x^2)) (A190215).

1, 2, 9, 48, 265, 1500, 8638, 50360, 296325, 1756160, 10467556, 62683896, 376838098, 2272896626, 13747543035, 83354081728, 506467851061, 3083121435312, 18799746616104, 114804614071760, 702016963933404, 4297947201746176, 26342178216979384

Offset: 0

Author

Emanuele Munarini, May 10 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)

Crossrefs

Cf. A190215.

Programs

Mathematica

Table[Sum[Binomial[n+i,n]Sum[Binomial[i+j-1,j]Binomial[j,n-i-j],{j,0,n-i}],{i,0,n}],{n,0,22}]

Maxima

makelist(sum(binomial(n+i,n)*sum(binomial(i+j-1,j)*binomial(j,n-i-j),j,0,n-i),i,0,n),n,0,22);

PARI

for(n=0,30, print1(sum(k=0,n, binomial(n+k,n)*sum(j=0,n-k, binomial(k+j-1,j)*binomial(j,n-k-j))), ", ")) \\ G. C. Greubel, Mar 04 2018

Formula

a(n) = T(2*n,n), where T(n,k)=A190215(n,k).

a(n) = Sum_{i=0..n} binomial(n+i,n)*Sum_{j=0..n-i} binomial(i+j-1,j)*binomial(j,n-i-j).